Spectral/hp element methods: recent developments, applications, and perspectives

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed

Encapsulation and Aggregation

A notion of object ownership is introduced as a solution to difficult problems of specifying and reasoning about complex linked structures and of modeling aggregates (composit objects). Syntax and semantics are provided for extending Eiffel with language support for object ownership annotation and checking. The ideas also apply to other OOPLs such as C++

Type Classes for Lightweight Substructural Types

Linear and substructural types are powerful tools, but adding them to standard functional programming languages often means introducing extra annotations and typing machinery. We propose a lightweight substructural type system design that recasts the structural rules of weakening and contraction as type classes; we demonstrate this design in a prototype language, Clamp. Clamp supports polymorphic substructural types as well as an expressive system of mutable references. At the same time, it adds little additional overhead to a standard Damas-Hindley-Milner type system enriched with type classes. We have established type safety for the core model and implemented a type checker with type inference in Haskell.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441

A study of real-time computer graphic display technology for aeronautical applications

Hardware, algorithms and software for real-time raster graphics were designed and implemented